平面区域有限元三角网格迭代优化方法  

Iterative Optimization Method of Finite Element Triangle Mesh in Planar Area

作　　者：李宗领[1] 阎春平[1] 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400030

出　　处：《新型工业化》2013年第8期32-40,共9页The Journal of New Industrialization

基　　金：国家863计划资助项目(2012AA041306)

摘　　要：为了提高有限元分析计算结果的准确性,提出一种平面区域有限元三角网格迭代优化算法。该算法首先利用一种基于Loop模式的1-2细分方法来实现给定网格的局部细分;然后利用顶点自由度与边折叠相结合的新方法对细分后的网格进行简化;最后,基于正三角形为最优三角形的事实,提出一种最小角最大化方法对网格进行几何优化。算法的特点是在不同的阶段采用不同的评价标准对网格质量进行评价,即在网格细分和简化阶段采用边长法,而在几何优化阶段采用角度法。将该算法应用于建筑金属结构工程有限元分析系统,取得了较好的应用效果。To improve accuracy of finite element analysis results, an iterative optimization algorithm of finite element triangle mesh in planar area was proposed. Firstly, the algorithm uses 1-2 subdivision method based on Loop model to achieve local subdivision of a given mesh. Then the mesh is simplified in a new method which combines the degree of freedom and edge collapse. Finally, basing on the fact that the equilateral triangle is the best a method of minimum angle maximization is put forward to perform the geometry optimization. The characteristic of the algorithm is using different evaluation criterion to evaluate the mesh equality, that is to say, method of side length is adopted in the subdivision and simplification stage, while angle method is adopted in the geometry optimization stage. A favorable result is demonstrated when applying the algorithm to an engineering product analysis system for the metal construction.

关 键 词：有限元分析 三角网格 网格优化 网格细分 网格几何优化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]